Question

Marie, jordan, cristina, gabriel, cristian, eliana, and kamel have all been invited to a dinner party. they arrive randomly and each person arrives at a different time. find the probability that eliana arrives first and cristian arrives last. write your answer as a simplified fraction.

Answer 1

The probability that Eliana arrives first and Cristian arrives last is 1/42.

Step-by-step explanation:

To determine the probability that Eliana will arrive first and Cristian will arrive last to the dinner party, we need to consider the total number of people invited and the specific positions we are trying to calculate the probability for. There are 7 people invited, so the total number of possible arrangements for their arrival is 7 factorial (7!). For Eliana to arrive first, there is only 1 way this can happen, as it specifically involves her. For Cristian to arrive last, again, there is only 1 way this can occur. The other five guests can arrive in any order, so there are 5 factorial (5!) ways to arrange them.

By calculating these values, we find that 5! = 120, and 7! = 5! × 6 × 7 = 120 × 42 = 5040. The probability of Eliana arriving first and Cristian last is the number of favorable outcomes (120) divided by the total possible outcomes (5040), resulting in 120/5040 which simplifies to 1/42.